Contrasting three alternative versions of Timoshenko‐Ehrenfest theory for beam on Winkler elastic foundation – simply supported beam

Abstract

In this paper the free vibration frequencies of beam on one‐parameter (Winkler) elastic foundation are analyzed via original Timoshenko‐Ehrenfest theory as well as two truncated versions of the Timoshenko‐Ehrenfest beam theory. The traditional version of Timoshenko‐Ehrenfest beam theory is contrasted with the truncated version that lacks the fourth‐order time derivative, as well as with the recently developed version that incorporates slope inertia effect. Advantages and disadvantages of each approach are indicated in the context of free vibrations of the beam on Winkler foundation. In addition an intriguing intermingling phenomenon is discussed in detail, and its implications on three theories.

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

“…An important initial motivation for dynamic analysis originates from the needs of railway engineering in the evaluation of the effect of moving loads [7]. In this case, apart from the aforementioned Euler-Bernoulli beam theory, refined Timoshenko-type formulations have also been adapted, see, e.g., [8][9][10][11]; and also more recent publications concerned with harmonic vibrations of a Timoshenko-type beam supported by a Winkler foundation, see [12,13].…”

Dispersion of elastic waves in a layer interacting with a Winkler foundation

“…It still finds numerous applications including modelling of transit and edge bending waves, (Brun et al, 2013), (Kaplunov et al, 2016b), (Kaplunov et al, 2014), see also (Kaplunov and Nobili, 2017a) using refined Pasternak model. Among the publications on the subject we also mention (Elishakoff et al, 2018;Li et al, 2009;Ponnusamy and Selvamani, 2012).…”

Calculation and Analysis of Pipe Joint Settlement Control in Large Back Silting Immersed Tube Tunnel

“…However, since the springs operated independently of each other, they only provided local resistance at the point of loading and failed to generate resistance elsewhere [25]. Numerous achievements were proposed based on this model [26][27][28][29][30][31][32][33], deducing and calculating the stress and deformation of the structural system of immersed tube tunnels under the action of uneven soil layers and analyzing the sensitivity of various influencing factors to the settlement, in addition to obtaining a set of reasonable calculation methods for settlement control standards of segmental immersed tube tunnels. The research results provide a favorable scientific basis for the optimization of the tunnel foundation scheme and the improvement of the construction technology to ensure the safety of the structure to a greater extent.…”